On identification of discrete symmetric planar shapes from a single view

In this paper, we consider a problem of identifying a discrete symmetric shape from a single view. For the proposed class of objects, we derive their representation in terms of their "skeletons", which in turn yield invariants readily computable from any single image. In addition, the representation is almost optimal in the sense that it captures virtually all geometric information contained in the image. Further, we consider the case of a noisy image, i.e. when the points defining a shape are known up to an additive Gaussian noise. We derive the distribution for the noisy "skeleton" points and propose an optimal technique to estimate the true "skeleton" and thus identify the true shape.